I receive first email and take an action to constitute a field update to "engaged"

After 2 days, the automation flow is set to send email 2 > Do I receive the email from this flow I started in? Or does the system automatically recheck the field before the next send and remove me from the series?

I think for what (I think) you are describing above, the best thing to do would be to create a Segment based on the "interested" field. Once a contact has been marked "interested" the workflow would look at that Segment in the Audience section of the workflow and begin the series for anyone that has that field marked "interested". Once the field is changed to read "engaged" it would remove the person from that Segment and the workflow.

If there is a series that they should receive after moving to "engaged" then you would set up that workflow separately, with the "engaged" Segment set up as the Audience to pay attention to in that workflow.

Field change triggers currently only watch for changes made via an “Add or update” call from the API (members/add or members/signup) or from manual updates to individual contact records in the contact section of the account. Keep in mind that Emma signup forms use the "Add" call to update audience member records, so fields updated via signup form can also trigger a field change automation workflow. Note: We plan to introduce coverage for changes that come from spreadsheets in the future, including both spreadsheet imports in the app or via the /members api call.